Question

find the solution
3x2 - x - 5 = 0

Answer 1

solutions....

Answer 2

Use the quadratic equation:\[x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\] I'll just go ahead and let you know that you WILL need to memorize this equation if you're in school.

In this case, a=3, b=(-1), and c=5

Answer 3

i've noticed, i always end up messing it up though.

Answer 4

i really don't understand exactly how to plug in the numbers. i don't understand which ones should be negative or positive. could you show me?

Answer 5

Basically, if you were to remove all the x's from the equation, you would be left with just coefficients (the boxed parts here):


Each term/coefficient has a sign (positive or negative) and a number. The number's sign is always to the left of the number. Generally, the positive sign is omitted if there are no terms before it, but you just need to remember that it's there. The same thing goes for 1's. For example, your equation has "-x" in it. Really, that is "-1x", but traditionally the number is omitted if it is just 1.

As far as how you use these numbers in the quadratic equation, you literally just replace each letter with its corresponding coefficient, INCLUDING its sign (positive or negative). You should also know your order of operations (GEMDAS) because that can effect how you evaluate the equation or put it into a calculator. For example, in the quadratic equation, it has "b^2". When you replace the b with "-1", you have to remember that groupings are evaluated before exponents. By replacing b with "-1", the "-1" is automatically assumed to be within its own parentheses, so you should end up with "(-1)^2". This is important because "(-1)^2" evaluates to "1", whereas "-1^2" evaluates to "-1".